Question

cos 72 = 6/x
tan 72 = 6/x
sin 72 = 6/x
which is the correct set up to solve for x?

Explanation:

Step1: Recall cosine - ratio in right - triangle

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Given an angle of $72^{\circ}$, if the side adjacent to the $72^{\circ}$ angle is 6 and the hypotenuse is $x$, then $\cos72^{\circ}=\frac{6}{x}$.

Step2: Analyze other trigonometric ratios

The tangent ratio is $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ and the sine ratio is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. They do not match the given side - relationship for this problem.

Answer:

$\cos72 = 6/x$